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    <title>hess</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>hess</b> -  Hessenberg form</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>H = hess(A)  </tt>
      </dd>
      <dd>
        <tt>[U,H] = hess(A)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A</b>
        </tt>: real or complex square matrix</li>
      <li>
        <tt>
          <b>H</b>
        </tt>: real or complex square matrix</li>
      <li>
        <tt>
          <b>U</b>
        </tt>: orthogonal or unitary square matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>[U,H] = hess(A)</b>
      </tt> produces a unitary matrix
    <tt>
        <b>U</b>
      </tt> and a Hessenberg matrix <tt>
        <b>H</b>
      </tt> so that
    <tt>
        <b>A = U*H*U'</b>
      </tt> and <tt>
        <b>U'*U</b>
      </tt> =
    Identity.  By itself, <tt>
        <b>hess(A)</b>
      </tt> returns <tt>
        <b>H</b>
      </tt>.</p>
    <p>
    The Hessenberg form of a matrix is zero below the first
    subdiagonal. If the matrix is symmetric or Hermitian, the form is
    tridiagonal.</p>
    <h3>
      <font color="blue">References</font>
    </h3>
    <dl>
      <p>
  hess function is based on the Lapack routines
 DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the complex case.</p>
    </dl>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=rand(3,3);[U,H]=hess(A);
and( abs(U*H*U'-A)&lt;1.d-10 )
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="qr.htm">
        <tt>
          <b>qr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../control/contr.htm">
        <tt>
          <b>contr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="schur.htm">
        <tt>
          <b>schur</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Used Function</font>
    </h3>
    <p>
      <tt>
        <b>hess</b>
      </tt> function is based on the Lapack routines
  DGEHRD, DORGHR for  real matrices and  ZGEHRD, ZORGHR for the
  complex  case.</p>
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